Solution of inequality x-3/x+7 < 0 is?
- [-7,3]
- (-7) < (3)
- (10-7)
- (-7,3)
Explanation
To solve the inequality x−3/x+7 < 0, we need to find where the expression is negative.
We first determine the critical points by setting the numerator and denominator equal to zero:
x−3 = 0 gives x = 3, and x+7 = 0 gives x = −7.
Now, we create a sign chart with these critical points and test intervals to see where the expression is negative:
Test x = −8 (a number less than -7): −8−3/-8+7 = −11/-1 = 11>0 (positive)
Test x = 0 (a number between -7 and 3): 0−3/0+7 = −3/7 <0 (negative)
Test x = 4 (a number greater than 3): 4−3/ 4+7 = 1/11 >0 (positive)
From this, we see the expression is negative when x is between -7 and 3, so the solution is (−7,3).
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